Description:
The event times are observed of a mixture of two kinds of radioactive atoms, each producing alpha particles. The probability of observing an event is p, 0 < p < 1, and of missing the observation is 1 - p. A maximum likelihood statistical method is given for estimating the size of the two populations. A second discussion assumes that the populations themselves are samples from parent populations. Bayesian methods are given for estimating parameters of the parent populations. An example is presented of an experiment involving the search for particle-bound polyneutron systems. 2 figures, 3 tables.

Description:
A method of probabilistic modeling of fault tree logic combined with stochastic process theory (Markov modeling) has been developed. Systems are then quantitatively analyzed probabilistically in terms of their failure mechanisms including common cause/common mode effects and time dependent failure and/or repair rate effects that include synergistic and propagational mechanisms. The modeling procedure results in a state vector set of first order, linear, inhomogeneous, differential equations describing the time dependent probabilities of failure described by the fault tree. The solutions of this Failure Mode State Variable (FMSV) model are cumulative probability distribution functions of the system. A method of appropriate synthesis of subsystems to form larger systems is developed and applied to practical nuclear power safety systems.